Digital Forensics Dr Bhavani Thuraisingham The University of

Digital Forensics Dr. Bhavani Thuraisingham The University of Texas at Dallas Validation and Recovering Graphic Files and Steganography September 20, 2013

Outline l Topics for Lecture - What data to collect and analyze - Validating forensics data - Data hiding techniques - Remote acquisitions - Recovering Graphic files - Data compression - Locating and recovering graphic files - Steganography and Steganalysis - http: //www. fbi. gov/hq/lab/fsc/backissu/july 2004/research/2 004_03_research 01. htm

What data to collect and analyze l Depends on the type of investigation l Email investigation will involve network logs, email server backups l Industrial espionage may include collecting information from cameras, keystrokes l Scope creep: Investigation extends beyond the original description due to unexpected evidence

Validating forensic data l Validating with hexadecimal editors - Provides support such as hashing files and sectors l Discriminating functions - Selecting suspicious data from normal data l Validating with forensics programs - Use message digests, hash values

Data Hiding l Data hiding is about changing or manipulating a file to conceal information l Hiding partitions: Create partitions and use disk editor to delete reference to it, then recreate links to find the partition l Marking bad clusters: Placing sensitive or incriminating data in free space; use disk editors to mark good clusters as bad clusters l But shifting: Change bit patterns or alter byte values l Using Stereography to hide data l Encrypt files to prevent access l Recover passwords using passwords recovery tools

Remote Acquisitions l Tools are available for acquiring data remotely - E. g. , Diskexplorer for FAT - Diskexporer for NTFS l Steps to follow - Prepare the tool for remote acquisition - Make remote connection - Acquire the data

Recovering Graphic Files l What are graphic files - Bitmaps and Raster images - Vector graphics - Metafile graphics l Graphics file formats - Standards and Specialized l Digital camera file formats - Raw and Inage file format

Data Compression l Lossless compression - Reduce file size without removing data l Lossy compression - Reduces file size but some bits are removed - JPEG l Techniques are taught in Image processing courses

Locating and Recovering Graphic Files l Identify the graphic file fragments - If the file is fragmented, need to recover all the fragments carving or salvaging) l Repair damage headers If header data is partially overwritten need to figure out what the missing pieces are l Procedures also exist form recovering digital photograph evidence l Steps to follow Identify file Recover damage headers Reconstruct file fragments Conduct exam - -

Steganography: Outline l Steganography l Null Ciphers l Digital Image and Audio l Digital Carrier Methods l Detecting Steganography l Tools l Reference: http: //www. fbi. gov/hq/lab/fsc/backissu/july 2004/research/2004 _03_research 01. htm

Steganography l Steganography is the art of covered or hidden writing. l The purpose of steganography is covert communication to hide a message from a third party. l This differs from cryptography, the art of secret writing, which is intended to make a message unreadable by a third party but does not hide the existence of the secret communication. l Although steganography is separate and distinct from cryptography, there are many analogies between the two, and some authors categorize steganography as a form of cryptography since hidden communication is a form of secret writing l We will treat steganography as a separate field.

Steganography - II l Steganography hides the covert message but not the fact that two parties are communicating with each other. l The steganography process generally involves placing a hidden message in some transport medium, called the carrier. l The secret message is embedded in the carrier to form the steganography medium. l The use of a steganography key may be employed for encryption of the hidden message and/or for randomization in the steganography scheme. l In summary: steganography_medium = hidden_message + carrier + steganography_key -

Taxonomy

Taxonomy l Technical steganography uses scientific methods to hide a message, such as the use of invisible ink or microdots and other size-reduction methods. ‘ l Linguistic steganography hides the message in the carrier in some nonobvious ways and is further categorized as semagrams or open codes. l Semagrams hide information by the use of symbols or signs. A visual semagram uses innocent-looking or everyday physical objects to convey a message, such as doodles or the positioning of items on a desk or Website. A text semagram hides a message by modifying the appearance of the carrier text, such as subtle changes in font size or type, adding extra spaces, or different flourishes in letters or handwritten text. -

Taxonomy l Open codes hide a message in a legitimate carrier message in ways that are not obvious to an unsuspecting observer. l The carrier message is sometimes called the overt communication, whereas the hidden message is the covert communication. l This category is subdivided into jargon codes and covered ciphers. l Jargon code uses language that is understood by a group of people but is meaningless to others. l Jargon codes include warchalking (symbols used to indicate the presence and type of wireless network signal underground terminology, or an innocent conversation that conveys special meaning because of facts known only to the speakers. l A subset of jargon codes is cue codes, where certain prearranged phrases convey meaning.

Taxonomy l Covered or concealment ciphers hide a message openly in the carrier medium so that it can be recovered by anyone who knows the secret for how it was concealed. l A grille cipher employs a template that is used to cover the carrier message. l The words that appear in the openings of the template are the hidden message. l A null cipher hides the message according to some prearranged set of rules, such as "read every fifth word" or "look at the third character in every word. "

Steganography vs Watermarking l On computers and networks, steganography applications allow for someone to hide any type of binary file in any other binary file, although image and audio files are today's most common carriers. l Steganography provides some very useful and commercially important functions in the digital world, most notably digital watermarking. l In this application, an author can embed a hidden message in a file so that ownership of intellectual property can later be asserted and/or to ensure the integrity of the content. l An artist, for example, could post original artwork on a Website. If someone else steals the file and claims the work as his or her own, the artist can later prove ownership because only he/she can recover the watermark

Steganography vs Watermarking l Although conceptually similar to steganography, digital watermarking usually has different technical goals. l Generally only a small amount of repetitive information is inserted into the carrier, it is not necessary to hide the watermarking information, and it is useful for the watermark to be able to be removed while maintaining the integrity of the carrier. l Steganography has a number of applications; most notably hiding records of illegal activity, financial fraud, industrial espionage, and communication among members of criminal or terrorist organizations

Null Cipher l Historically, null ciphers are a way to hide a message in another without the use of a complicated algorithm. One of the simplest null ciphers is shown in the classic examples below: l PRESIDENT'S EMBARGO RULING SHOULD HAVE IMMEDIATE NOTICE. GRAVE SITUATION AFFECTING INTERNATIONAL LAW. STATEMENT FORESHADOWS RUIN OF MANY NEUTRALS. YELLOW JOURNALS UNIFYING NATIONAL EXCITEMENT IMMENSELY. l APPARENTLY NEUTRAL'S PROTEST IS THOROUGHLY DISCOUNTED AND IGNORED. ISMAN HARD HIT. BLOCKADE ISSUE AFFECTS PRETEXT FOR EMBARGO ON BYPRODUCTS, EJECTING SUETS AND VEGETABLE OILS. l The German Embassy in Washington, DC, sent these messages in telegrams to their headquarters in Berlin during World War I. Reading the first character of every word in the first message or the second character of every word in the second message will yield the following hidden text: l PERSHING SAILS FROM N. Y. JUNE 1

Null Cipher l On the Internet, spam is a potential carrier medium for hidden messages. Consider the following: l Dear Friend , This letter was specially selected to be sent to you ! We will comply with all removal requests ! This mail is being sent in compliance with Senate bill 1621 ; Title 5 ; Section 303 ! Do NOT confuse us with Internet scam artists. Why work for somebody else when you can become rich within 38 days ! Have you ever noticed the baby boomers are more demanding than their parents & more people than ever are surfing the web ! Well, now is your chance to capitalize on this ! WE will help YOU sell more & SELL MORE. You can begin at absolutely no cost to you ! But don't believe us ! Ms Anderson who resides in Missouri tried us and says "My only problem now is where to park all my cars". This offer is 100% legal. You will blame yourself forever if you don't order now ! Sign up a friend and your friend will be rich too. Cheers ! Dear Salaryman , Especially for you - this amazing news. If you are not interested in our publications and wish to be removed from our lists, simply do NOT respond and ignore this mail ! This mail is being sent in compliance with Senate bill 2116 , Title 3 ; Section 306 !

Null Cipher l This is a ligitimate business proposal ! Why work for somebody else when you can become rich within 68 months ! Have you ever noticed more people than ever are surfing the web and nobody is getting any younger ! Well, now is your chance to capitalize on this. We will help you decrease perceived waiting time by 180% and SELL MORE. The best thing about our system is that it is absolutely risk free for you ! But don't believe us ! Mrs Ames of Alabama tried us and says "My only problem now is where to park all my cars". We are licensed to operate in all states ! You will blame yourself forever if you don't order now ! Sign up a friend and you'll get a discount of 20% ! Thanks ! Dear Salaryman , Your email address has been submitted to us indicating your interest in our briefing ! If you no longer wish to receive our publications simply reply with a Subject: of "REMOVE" and you will immediately be removed from our mailing list. This mail is being sent in compliance with Senate bill 1618 , Title 6 , Section 307. THIS IS NOT A GET RICH SCHEME. Why work for somebody else when you can become rich within 17 DAYS ! Have you ever noticed more people than ever are surfing the web and more people than ever are surfing the web !

Null Cipher l Well, now is your chance to capitalize on this ! WE will help YOU turn your business into an E-BUSINESS and deliver goods right to the customer's doorstep ! You are guaranteed to succeed because we take all the risk ! But don't believe us. Ms Simpson of Wyoming tried us and says "Now I'm rich, RICH" ! We assure you that we operate within all applicable laws. We implore you - act now ! Sign up a friend and you'll get a discount of 50%. Thank-you for your serious consideration of our offer. l This message looks like typical spam, which is generally ignored and discarded. This message was created at spam mimic, a Website that converts a short text message into a text block that looks like spam using a grammarbased mimicry idea first proposed by Peter Wayner. The reader will learn nothing by looking at the word spacing or misspellings in the message. The zeros and ones are encoded by the choice of the words. The hidden message in the spam carrier above is: l Meet at Main and Willard at 8: 30

Null Cipher l Special tools or skills to hide messages in digital files using variances of a null cipher are not necessary. l An image or text block can be hidden under another image in a Power. Point file, for example. l Messages can be hidden in the properties of a Word file. l Messages can be hidden in comments in Web pages or in other formatting vagaries that are ignored by browsers l Text can be hidden as line art in a document by putting the text in the same color as the background and placing another drawing in the foreground. l The recipient could retrieve the hidden text by changing its color. l These are essentially low-tech mechanisms, but they can be very effective.

Digital Image and Audio l Many common digital steganography techniques employ graphical images or audio files as the carrier medium. l Most digital image applications today support 24 -bit true color, where each picture element (pixel) is encoded in 24 bits, comprising the three RGB bytes as described above. l Other applications encode color using eight bits/pix. These schemes also use 24 -bit true color but employ a palette that specifies which colors are used in the image. Each pix is encoded in eight bits, where the value points to a 24 -bit color entry in the palette. This method limits the unique number of colors in a given image to 256 (2^8). l The choice color encoding obviously affects image size. A 640 X 480 pixel image using eight-bit color would occupy approximately 307 KB (640 X 480 = 307, 200 bytes), whereas a 1400 X 1050 pix image using 24 -bit true color would require 4. 4 MB (1400 X 1050 X 3 = 4, 410, 000 bytes).

Digital Image and Audio l Color palettes and eight-bit color are commonly used with Graphics Interchange Format (GIF) and Bitmap (BMP) image formats. GIF and BMP are generally considered to offer lossless compression because the image recovered after encoding and compression is bit-for-bit identical to the original image l The Joint Photographic Experts Group (JPEG) image format uses discrete cosine transforms rather than a pix-by-pix encoding. In JPEG, the image is divided into 8 X 8 blocks for each separate color component. The goal is to find blocks where the amount of change in the pixel values (the energy) is low. If the energy level is too high, the block is subdivided into 8 X 8 subblocks until the energy level is low enough. Each 8 X 8 block (or subblock) is transformed into 64 discrete cosine transforms coefficients that approximate the luminance (brightness, darkness, and contrast) and chrominance (color) of that portion of the image.

Digital Image and Audio l JPEG is generally considered to be lossy compression because the image recovered from the compressed JPEG file is a close approximation of, but not identical to, the original l Audio encoding involves converting an analog signal to a bit stream. Analog sound-voice and music-is represented by sine waves of different frequencies. The human ear can hear frequencies nominally in the range of 20 -20, 000 cycles/second (Hertz or Hz). l Sound is analog, meaning that it is a continuous signal. Storing the sound digitally requires that the continuous sound wave be converted to a set of samples that can be represented by a sequence of zeros and ones.

Digital Image and Audio l Analog-to-digital conversion is accomplished by sampling the analog signal (with a microphone or other audio detector) and converting those samples to voltage levels. The voltage or signal level is then converted to a numeric value using a scheme called pulse code modulation. The device that performs this conversion is called a coder-decoder or codec. l Pulse code modulation provides only an approximation of the original analog signal. If the analog sound level is measured at a 4. 86 level, for example, it would be converted to a five in pulse code modulation. This is called quantization error. Different audio applications define a different number of pulse code modulation levels so that this "error" is nearly undetectable by the human ear. The telephone network converts each voice sample to an eight-bit value (0 -255), whereas music applications generally use 16 -bit values (065, 535)

Digital Image and Audio l Analog signals need to be sampled at a rate of twice the highest frequency component of the signal so that the original can be correctly reproduced from the samples alone. In the telephone network, the human voice is carried in a frequency band 0 -4000 Hz (although only about 400 -3400 Hz is actually used to carry voice); therefore, voice is sampled 8, 000 times per second (an 8 k. Hz sampling rate). Music audio applications assume the full spectrum of the human ear and generally use a 44. 1 k. Hz sampling rate l The bit rate of uncompressed music can be easily calculated from the sampling rate (44. 1 k. Hz), pulse code modulation resolution (16 bits), and number of sound channels (two) to be 1, 411, 200 bits per second. This would suggest that a one-minute audio file (uncompressed) would occupy 10. 6 MB (1, 411, 200*60/8 = 10, 584, 000). Audio files are, in fact, made smaller by using a variety of compression techniques. One obvious method is to reduce the number of channels to one or to reduce the sampling rate, in some cases as low as 11 k. Hz. Other codecs use proprietary compression schemes. All of these solutions reduce the quality of the sound.

Digital Carrier Methods l There are many ways in which messages can be hidden in digital media. Digital forensics examiners are familiar with data that remains in file slack or unallocated space as the remnants of previous files, and programs can be written to access slack and unallocated space directly. Small amounts of data can also be hidden in the unused portion of file headers l Information can also be hidden on a hard drive in a secret partition. A hidden partition will not be seen under normal circumstances, although disk configuration and other tools might allow complete access to the hidden partition l This theory has been implemented in a steganographic ext 2 fs file system for Linux. A hidden file system is particularly interesting because it protects the user from being tied to certain information on their hard drive.

Digital Carrier Methods l This form of plausible deniability allows a user to claim to not be in possession of certain information or to claim that certain events never occurred. Under this system users can hide the number of files on the drive, guarantee the secrecy of the files' contents, and not disrupt nonhidden files by the removal of the steganography file driver ( l Another digital carrier can be the network protocols. Covert Transmission Control Protocol by Craig Rowland, for example, forms covert communications channels using the identification field in Internet Protocol packets or the sequence number field in Transmission Control Protocol segments l There are several characteristics of sound that can be altered in ways that are indiscernible to human senses, and these slight alterations, such as tiny shifts in phase angle, speech cadence, and frequency, can transport hidden information

Digital Carrier Methods l Image and audio files remain the easiest and most common carrier media on the Internet because of the plethora of potential carrier files already in existence, the ability to create an infinite number of new carrier files, and the easy access to steganography software that will operate on these carriers. . l The most common steganography method in audio and image files employs some type of least significant bit substitution or overwriting. The least significant bit term comes from the numeric significance of the bits in a byte. The high-order or most significant bit is the one with the highest arithmetic value (i. e. , 27=128), whereas the low-order or least significant bit is the one with the lowest arithmetic value (i. e. , 20=1).

Digital Carrier Methods l As a simple example of least significant bit substitution, imagine "hiding" the character 'G' across the following eight bytes of a carrier file (the least significant bits are underlined): l 10010101 00001101 110010010110 00001111 11001011 10011111 00010000 l A 'G' is represented in the American Standard Code for Information Interchange (ASCII) as the binary string 01000111. These eight bits can be "written" to the least significant bit of each of the eight carrier bytes as follows: l 10010100 00001101 11001000 10010110 00001110 11001011 10011111 0001 l In the sample above, only half of the least significant bits were actually changed (shown above in italics). This makes some sense when one set of zeros and ones are being substituted with another set of zeros and ones.

Digital Carrier Methods l Least significant bit substitution can be used to overwrite legitimate RGB color encodings or palette pointers in GIF and BMP files, coefficients in JPEG files, and pulse code modulation levels in audio files. By overwriting the least significant bit, the numeric value of the byte changes very little and is least likely to be detected by the human eye or ear. l Least significant bit substitution is a simple, albeit common, technique for steganography. Its use, however, is not necessarily as simplistic as the method sounds. Only the most naive steganography software would merely overwrite every least significant bit with hidden data. Almost all use some sort of means to randomize the actual bits in the carrier file that are modified. This is one of the factors that makes steganography detection so difficult. l One other way to hide information in a paletted image is to alter the order of the colors in the palette or use least significant bit encoding on the palette colors rather than on the image data. These methods are potentially weak, however. Many graphics software tools order the palette colors by frequency, luminance, or other parameter, and a randomly ordered palette stands out under statistical analysis

Digital Carrier Methods l Newer, more complex steganography methods continue to emerge. l Spread-spectrum steganography methods are analogous to spread- spectrum radio transmissions (developed in World War II and commonly used in data communications systems today) where the "energy" of the signal is spread across a wide-frequency spectrum rather than focused on a single frequency, in an effort to make detection and jamming of the signal harder. l Spread-spectrum steganography has the same function—avoid detection. l These methods take advantage of the fact that little distortions to image and sound files are least detectable in the high-energy portions of the carrier (i. e. , high intensity in sound files or bright colors in image files). Even when viewed side by side, it is easier to fool human senses when small changes are made to loud sounds and/or bright colors

Detecting Steganography l Steganalysis, the detection of steganography by a third party, is a relatively young research discipline with few articles appearing before the late-1990 s. l The art and science of steganalysis is intended to detect or estimate hidden information based on observing some data transfer and making no assumptions about the steganography algorithm l Detection of hidden data may not be sufficient. The steganalyst may also want to extract the hidden message, disable the hidden message so that the recipient cannot extract it, and/or alter the hidden message to send misinformation to the recipient l Steganography detection and extraction is generally sufficient if the purpose is evidence gathering related to a past crime, although destruction and/or alteration of the hidden information might also be legitimate law enforcement goals during an ongoing investigation of criminal or terrorist groups.

Detecting Steganography l Steganalysis techniques can be classified in a similar way as cryptanalysis methods, largely based on how much prior information is known - Steganography-only attack: The steganography medium is the only item available for analysis. - Known-carrier attack: The carrier and steganography media are both available for analysis. - Known-message attack: The hidden message is known. - Chosen-steganography attack: The steganography medium and algorithm are both known. - Chosen-message attack: A known message and steganography algorithm are used to create steganography media for future analysis and comparison. - Known-steganography attack: The carrier and steganography medium, as well as the steganography algorithm, are known.

Detecting Steganography l Steganography methods for digital media can be broadly classified as operating in the image domain or transform domain. Image domain tools hide the message in the carrier by some sort of bit-by-bit manipulation, such as least significant bit insertion. l Transform domain tools manipulate the steganography algorithm and the actual transformations employed in hiding the information, such as the discrete cosine transforms coefficients in JPEG images l Steganalysis broadly follows the way in which the steganography algorithm works. l One simple approach is to visually inspect the carrier and steganography media. l Many simple steganography tools work in the image domain and choose message bits in the carrier independently of the content of the carrier. l Although it is easier to hide the message in the area of brighter color or louder sound, the program may not seek those areas out. Thus, visual inspection may be sufficient to cast suspicion on a steganography medium

Detecting Steganography l A second approach is to look for structural oddities that suggest manipulation. Least significant bit insertion in a palette-based image often causes a large number of duplicate colors, where identical (or nearly identical) colors appear twice in the palette and differ only in the least significant bit. l Steganography programs that hide information merely by manipulating the order of colors in the palette cause structural changes, as well. The structural changes often create a signature of the steganography algorithm that was employed l Steganographic techniques generally alter the statistics of the carrier and, obviously, longer hidden messages will alter the carrier more than shorter ones

Detecting Steganography l Statistical analysis is commonly employed to detect hidden messages, particularly when the analyst is working in the blind l Statistical analysis of image and audio files can show whether the statistical properties of the files deviate from the expected norm l These so-called first-order statistics—means, variances, chi-square (Χ 2) tests—can measure the amount of redundant information and/or distortion in the medium. l Although these measures can yield a prediction as to whether the contents have been modified or seem suspicious, they are not definitive l Statistical steganalysis is made harder because some steganography algorithms take pains to preserve the carrier file's first-order statistics to avoid just this type of detection. Encrypting the hidden message also makes detection harder because encrypted data generally has a high degree of randomness, and ones and zeros appear with equal likelihood

Detecting Steganography l Recovery of the hidden message adds another layer of complexity compared to merely detecting the presence of a hidden message. Recovering the message requires knowledge or an estimate of the message length and, possibly, an encryption key and knowledge of the crypto algorithm l Carrier file type-specific algorithms can make the analysis more straightforward. l JPEG, in particular, has received a lot of research attention because of the way in which different algorithms operate on this type of file. l JPEG is a poor carrier medium when using simple least significant bit insertion because the modification to the file caused by JPEG compression eases the task of detecting the hidden information

Detecting Steganography l There are several algorithms that hide information in JPEG files, and all work differently. JSteg sequentially embeds the hidden data in least significant bits JP Hide&Seek uses a random process to select least significant bits, F 5 uses a matrix encoding based on a Hamming code, and Out. Guess preserves first-order statistics l More advanced statistical tests using higher-order statistics, linear analysis, Markov random fields, wavelet statistics, and more on image and audio files have been described -

Detecting Steganography l Most steganalysis today is signature-based, similar to antivirus and intrusion detection systems. l Anomaly-based steganalysis systems are just beginning to emerge. l Although the former systems are accurate and robust, the latter will be more flexible and better able to quickly respond to new steganography techniques. l One form of so-called "blind steganography detection" distinguishes between clean and steganography images using statistics based on wavelet decomposition, or the examination of space, orientation, and scale across subsets of the larger image l This type of statistical steganalysis is not limited to image and audio files.

Detecting Steganography l The Hydan program retains the size of the original carrier but, by using sets of "functionally equivalent" instructions, employs some instructions that are not commonly used. l This opens Hydan to detection when examining the statistical distribution of a program's instructions. l Future versions of Hydan will maintain the integrity of the statistical profile of the original application to defend against this analysis l The law enforcement community does not always have the luxury of knowing when and where steganography has been used or the algorithm that has been employed. l Generic tools that can detect and classify steganography are where research is still in its infancy but are already becoming available in software tools l And the same cycle is recurring as seen in the crypto world—steganalysis helps find embedded steganography but also shows writers of new steganography algorithms how to avoid detection.

Some Tools l The detection of steganography software on a suspect computer is important to the subsequent forensic analysis. l Many steganography detection programs work best when there are clues as to the type of steganography that was employed in the first place. l Finding steganography software on a computer would give rise to the suspicion that there actually steganography files with hidden messages on the suspect computer. l The type of steganography software found will directly impact any subsequent steganalysis (e. g. , S-Tools might direct attention to GIF, BMP, and WAV files, whereas JP Hide-&-Seek might direct the analyst to look more closely at JPEG files).

Some Tools l Wet. Stone Technologies' Gargoyle (formerly Stego. Detect) software can be used to detect the presence of steganography software. - Gargoyle employs a proprietary data set (or hash set) of all of the files in the known steganography software distributions, comparing them to the hashes of the files subject to search. Gargoyle data sets can also be used to detect the presence of cryptography, instant messaging, key logging, Trojan horse, password cracking l Access. Data's Forensic Toolkit and Guidance Software's En. Case can use the Hash. Keeper, Maresware, and National Software Reference Library hash sets to look for a large variety of software. - In general, these data sets are designed to exclude hashes of known "good" files from search indexes during the computer forensic analysis. Gargoyle can also import these hash sets.

Some Tools l Wet. Stone Technologies' Stego Watch analyzes a set of files and provides a probability about which are steganography media and the likely algorithm used for the hiding (which, in turn, provides clues as to the most likely software employed). - The analysis uses a variety of user-selectable statistical tests based on the carrier file characteristics that might be altered by the different steganography methods. Knowing the steganography software that is available on the suspect computer will help the analyst select the most likely statistical tests. l The Institute for Security Technology Studies at Dartmouth College has developed software capable of detecting hidden data in image files using statistical models that are independent of the image format or steganography technique. - This program has been tested on 1, 800 images and four different steganography algorithms and was able to detect the presence of hidden messages with 65 percent accuracy with a false-positive rate less than 0. 001 percent